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In this paper we consider a fundamental problem in the area of viral marketing , called TARGET SET SELECTION problem. We study the problem when the underlying graph is a block-cactus graph, a chordal graph or a Hamming graph. We show that if G is a block-cactus graph, then the TARGET SET SELECTION problem can be solved in linear time, which generalizes(More)
Distance-hereditary graphs are graphs in which every two vertices have the same distance in every connected induced subgraph containing them. This paper studies distance-hereditary graphs from an algorithmic viewpoint. In particular, we present linear-time algorithms for finding a minimum weighted connected dominating set and a minimum vertex-weighted(More)
The domination problem and its variants have been extensively studied in the literature. In this paper we investigate the domination problem in distance-hereditary graphs. In particular, we give a linear-time algorithm for the domination problem in distance-hereditary graphs by a labeling approach. We actually solve a more general problem, called the(More)
Let G be a graph with a threshold function θ : V (G) → N such that 1 ≤ θ(v) ≤ d G (v) for every vertex v of G, where d G (v) is the degree of v in G. Suppose we are given a target set S ⊆ V (G). The paper considers the following repetitive process on G. At time step 0 the vertices of S are colored black and the other vertices are colored white. After that,(More)
A graph is distance-hereditary if the distance between any two vertices in a connected induced subgraph is the same as in the original graph. In this paper, we study metric properties of distance-hereditary graphs. In particular, we determine the structures of centers and medians of distance-hereditary and related graphs. The relations between eccentricity,(More)
In this paper we consider a fundamental problem in the area of viral marketing , called TARGET SET SELECTION problem. In a a viral marketing setting, social networks are modeled by graphs with potential customers of a new product as vertices and friend relationships as edges, where each vertex v is assigned a threshold value θ(v). The thresholds represent(More)
It is shown that the difference between the chromatic number χ and the fractional chromatic number χ f can be arbitrarily large in the class of uniquely colorable, vertex transitive graphs. For the lexicographic product G • H it is shown that χ(G • H) ≥ χ f (G) χ(H). This bound has several consequences, in particular it unifies and extends several known(More)